Constraints on Operator Ordering from Third Quantization

TL;DR

This paper investigates how operator ordering choices in third quantization influence the quantum-to-classical transition of the universe, using the Wheeler-DeWitt equation and cosmological models to derive physical constraints.

Contribution

It demonstrates that physical requirements on quantum fluctuations can constrain operator ordering in third quantization, with explicit analysis on two cosmological models.

Findings

Quantum fluctuations dominate early universe stages.

Universe becomes classical during cosmic expansion.

Operator ordering constraints derived from physical considerations.

Abstract

In this paper, we analyse the Wheeler-DeWitt equation in the third quantized formalism. We will demonstrate that for certain operator ordering, the early stages of the universe are dominated by quantum fluctuations, and the universe becomes classical at later stages during the cosmic expansion. This is physically expected, if the universe is formed from quantum fluctuations in the third quantized formalism. So, we will argue that this physical requirement can be used to constrain the form of the operator ordering chosen. We will explicitly demonstrate this to be the case for two different cosmological models.